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a  h
From the figure we obtain cos a =
therefore                           sin a = - \/h (2 a  h),
and                                 F =  Vh(2a-h).
FIG. 35.
Since cos 6 = 0 the first equation of equilibrium gives
R  W cos a
DISCUSSION.  It will be observed that the first two of the equations of equilibrium are sufficient to solve the problem.
When h is zero, F = 0 and R = IF. On the other hand when h = a, F = W and R = 0.
1.   Prove that the true weight of a body is the geometric mean between the apparent weights obtained by weighing it in both pans of a false balance.
2.   A uniform bar weighing 10 pounds is supported at the ends.   A weight of 25 pounds is suspended from a point 20 cm. from one end. Find the pressure at the supports if the length of the bar is 50 cm.
3.   A uniform rod which rests on a rough horizontal floor and against a smooth vertical wall is on the point of slipping.   Find the reactions at the two ends of the rod.